Daily Practice · Higher Plus

Daily Practice - Higher Plus

Grades 8-9 - exam-stretch algebra, geometry and reasoning.

14th June 2025

5 questions · 14 marks · Grades 8-9 · 51 question types in this band

1
Completing the Square3 marks
Work out the coordinates of the turning point of y = x^2 - 14x - 2.
2
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^2. When x = 6, y = 324. Work out the positive value of x when y = 729.
3
Proof of the Circle Theorems2 marks
In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
4
Probability Equation Questions3 marks
A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
5
Histograms3 marks
A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?

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